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Chapter Seven Atomic Structure

Chapter Seven Atomic Structure. neutrons atoms protons ( positive charge ) electrons ( negative charge ). 7-1 Changing Ideas about Atomic Structure 7-2 The Quantum Mechanical Description of Electron in Hydrogen Atoms

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Chapter Seven Atomic Structure

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  1. Chapter SevenAtomic Structure neutrons • atomsprotons (positive charge ) electrons(negative charge)

  2. 7-1 Changing Ideas about Atomic Structure 7-2 The Quantum Mechanical Description of Electron in Hydrogen Atoms 7-3 Electron Configuration of Many- electron Atoms 7-4 The Periodic Table and Periodic Law

  3. 7-1.1 The Bohr theory of Hydrogen Atom • 1805 dolton proposed atom theory, proved exist of atom • 1900 electron were discovered • 1911 Ruthrford proposed the atomic nucleus by α-ray scatting • 1931 neutron were discovered

  4. Figure 7-1: In classical theory: 1.atoms constructed are not stable; 2.the electron would quickly spiral into the nucleus. 3. Not is the line spectra of atoms Ruthrford’s nuclear model

  5. Continuous spectrum

  6. Atomic Line Spectra Na

  7. （H、He、Li、Na、Ba、Hg、Ne light emission)

  8. In 1913, Niels Bohr(1885-1962), founded Bohr theory by using the work of Planck and Einstein

  9. Quantum of concept no continuum emission • Atom a copy of energy absord Least unit quantum

  10. The Photoelectric Effect Einstein used the quantum theory to explain the photoelectric effect : Each energy packet called photon, is a quantum of energy E=h v Physicist Albert Einstein (1879 -1955) h Planck’s constant = 6.623×10-34J s.

  11. （波粒二象性） E = hv = Photons of high frequency radiation have high energies, whereas photons of lower frequency radiation have lower energy.

  12. 7-1.1 The Bohr theory of Hydrogen Atom • Bohr set down the following • two postulates to account for: (1) the stability of the hydrogen atom (that the atom exists and its electron does not continuously radiate energy and spiral into the nucleus) (2) the line spectrum of the atom.

  13. Bohr theory of Hydrogen Atom • Bohr assumed that: 1.Energy-level postulate an atom looked something like the solar system: 1) a nucleus at the center 2) the electron could have only certain orbits L 代表电子运动轨道的角动量（L= p ·r =mv r ） P 是电子轨道运动动量， r 是轨道半径， m 是电子的质量， v 是电子的运动速度。 电子在任意轨道做圆周运动的角动量mv r 必须是 的整数倍， n = 1, 2, 3, 量子化条件：

  14. n=3 n=2 n=1 + r =52.9pm

  15. Bohr theory of Hydrogen Atom • 3)energy levels: an electron in an atom can have only specific energy values, which are called the energy levels of the electron in the atom En = - (Z2/n2) ×2.180 × 10-18J (for H atom) Z : 核电荷数 n : 能级数 1, 2, 3, --- ∞ n值越大，表示电子运动轨道离核越远，能量越高。

  16. 2. Transitions（跃迁）between energy levels • photons are given off or absorbed when an electron moves from one orbit to another. ground statea lower energy state ( if n = 1, is called ground state ) excited state a high energy state ( if n = 2、3……, is called ground state)

  17. Ground state Energy of emitted photon ΔE = Ei- Ef= hv Excited state Ei a higher energy level (initial energy level) Ef a lower energy level (final energy level )

  18. In 1885, J.J. Balmer showed that the wavelengths, λ, in the visible spectrum of hydrogen could be reproduced by a simple formula. 1 1 1 --- = 1.097 × 107m-1 ( ---- - -----) λ 2 2 n 2 postulate from level n = 4 to level n = 2 light of wavelength 486 nm (blue green )is emitted

  19. 6 High E Short l High n Low E Long l Low n 5 4 3 2 Energy 1 n Infrared Paschen Visible Balmer Ultra Violet Lyman Hydrogen atom spectra Visible lines in H atom spectrum are called the BALMERseries.

  20. Bohr’s theory • Successful 1.established the concept of atomic energy levels (atomic orbit) 2. explaining the spectrum of hydrogen • Unsuccessful 1. atomic orbit is fastness 2. can’t explain minuteness the spectrum of hydrogenatom

  21. 7-1.2 De Broglie Waves (Matter Waves) Louis-Victor de Broglie, (1892 -1987, France) In 1929, he was awarded the Nobel Prize for Physics for his research on quantum theory and his discovery of the wave nature of electrons. He showed that the wavelength of moving particlesis equal to Planck's constant divided by the momentum.

  22. （7-4） • Mass: >> h , • Particle: is short wave properties ignored <<h， can not ignored wave properties

  23. [例7－1] 分别计算m=2.5×10-2kg，v = 300m·s-1的子弹和me=9.1×10-31kg v =1.5×106 m·s-1的电子的 波长，并加以比较。 • 解： 按（7-4）式，子弹的波长为： 电子的波长为： 计算结果表明，子弹的波长很短，完全可以不予考虑。

  24. 电子的波粒二象性（Davisson和Germer实验 ） 1927年美国物理学家Davisson C和Germer L根据电子的波长 与X射线波长相近，用电子束代替X射线，用镍晶体薄层 作为光栅进行衍射实验，得到与X射线衍射类似的图像， 证实了电子的波动性。 electron diffracted X-diffracted

  25. 7-1.3 The Heisenberg Uncertainty principle • 1927 ,He recognized : no experimental method can be devised that will measure simultaneously the preciseposition(x) as well us the momentum (mv) of an object. Heisenberg German physicist (1901-1971)

  26. Uncertainty principle formula Δp uncertainty of the momentum Δx uncertainty of the position h Planck's constant The more precisely one knows Δp, the lessprecisely Δx is known, and vice versa.

  27. (中文p148_) Example • Suppose Δx=1.0 ×10- 4 m for a substance with mass of 0.01kg • In hydrogen atom, for an electron, v =106m/s , suppose Δx=1.0 ×10- 10m, 电子速度的不准确量 与其速度本身十分接近

  28. Quantum or Wave Mechanics Schrodinger applied idea of e-behaving as a wave to the problem of electrons in atoms. E the total energy Vthe potential energy m a particle in terms of its mass x y z respect to its position in three dimensions E. Schrodinger 1887-1961 1933 received the Nobel Prize

  29. 7-1.4 Schrődinger Equation(wave function) Solution to WAVE EQUATION gives set of mathematical expressions called WAVE FUNCTIONS ψ (psi) • wave function ψ has an amplitude（振幅）at each position in space (just as for a water wave or a classical electromagnetic wave).

  30. 7-2.1 Wave Function, Atomic Orbital andElectron Cloud ψ is a function of distance and two angles. ———Ψ(r,θ,φ)、 For 1 electron, ψ corresponds to an ORBITAL — the region of space within which an electron is found. ψdoes NOT describe the exact location of the electron.

  31. 7-2.2 Atomic Orbital ____ Quantum Numbers n the principal quantum number l the angular momentum quantum number m the magnetic quantum number. they will be used to describe atomic orbitals and to labelelectrons that reside in them.

  32. 1. Principal quantum number (n): • Shell K L M N . . . n 1 2 3 4 . . . As n increases, the orbitals extend farther from the nucleus,average position of an electronin these orbitals is farther from the nucleus Energies: K<L<M<N<O< … 1<2< 3< 4< 5 < …

  33. 2. Angular momentum quantum number (l) • Within each shell of quantum number n , there are n different kinds of orbital, each with a distinctive shape, denoted by the l quantum number. • subshells p d f g . . . l 0 1 2 3 4 . . .(n-l) Energies: s<p < d < f < g…

  34. 3. Magnetic quantum number (m): A subshell has the same shape, but a different orientation, or direction, in space. m = (2 l + 1)or Each orbital ofa particular subshell (no matter how it is oriented in space) has the same energy. Example: p orbit have 3 different orientation p x. p y p z

  35. About Quantum Numbers —— Orbital nl m An atomic orbital is defined by 3 quantum numbers: Electrons are arranged in shells and subshells of RBITALS . n  shell l  subshell m designates an orbital within a subshell

  36. Table 7-1:The allowed sets of quantum numbers for atomic orbitals

  37. 4. Spin quantum number (ms) : msthe spin quantum number refers to a magnetic property of electrons called spin. Values for the spin quantum number are +1/2 and –1/2.

  38. A fourth quantum number Note:n. l. m. ms they will be used to describe electrons that reside in them

  39. QUANTUMNUMBERS 1. Which of the following is not a valid set(有效的组合) of four quantum numbers to describe an electron in an atom? (1) 1, 0, 0, +½ (2) 2, 1, 1, +½ (3) 2, 0, 0, –½ (4) 1, 1, 0, +½ 2. The energy of an orbital in a many-electron atom depends on (1) the value of n only (2) the value of l only (3) the values of n and l (4) the values of n, l, and m

  40. 7-2.3 Sizes and Shapes of Atomic Orbitals Radial wave function angular wave function

  41. Spherical coordinates x = r sin cos y = rsin sin z = r cos

  42. Shapes of the orbitals • Shapes of the orbitals for: • (a) an s subshell • (b) a psubsell • (c) a d subshell ?

  43. 如：氢原子的角度部分 【s轨道】 Ys是一常数与(q,f)无关，半径为: 【pz轨道】 节面：当cosq = 0时，Ｙ=0，q = 90° 　　我们下来试做一下函数在Pz平面的图形。

  44. 30° + θ 60° － 0 30 60 90 节面：当θ= 90° cosθ= 0 Ｙ=0时

  45. 波函数的角度分布图 由图可知，原子轨道的角度分布图有正负之分，这对于讨论分子的化学键及对称性十分重要。 同样地，可以画出其它原子轨道的角度分布图。

  46. The Probability Function (ψ2) —— Electron Cloud ψ2is related to the probability per unit volume such that the product of ψ 2 and a small volume (called a volume element) yields the probability of finding the electron within that volume.

  47. 1. Electron Cloud • The total probability of locating the electron in a given volume (for example, around the nucleus of an atom) is then given by the sum of all the products of ψ2 and the corresponding volume elements.

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